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La structure géométrique des groupes stables. (The geometric structure of stable groups). (French) Zbl 0564.03031
This paper is a brief survey of the presently known methods of investigation of simple groups. Stability conditions impose some structural conditions on groups; the first one can be described as ”chain conditions on definable subsets”; the second one concerns the properties of ”large” definable subsets, the so-called ”generic subsets”, which arose from the efforts of B. Zilber to transfer some well-known properties of algebraic groups to the general case of stable groups; these methods culminate in the Indecomposability Lemma of Zilber.
03C45 Classification theory, stability and related concepts in model theory
03C60 Model-theoretic algebra
20E32 Simple groups